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Verify the following proposition with the help of a truth table:
Verify the following proposition with the help of a truth table:
$( P \land Q ) \lor ( P \land \sim Q ) = P$
Answer
Answer
AI$(P \land Q) \lor (P \land \sim Q) = P$
Truth table (verified with the boolean tool):
The column for $(P \land Q) \lor (P \land \sim Q)$ is identical to the column for $P$ in every row. Hence the proposition is verified: $(P \land Q) \lor (P \land \sim Q) = P$.
| P | Q | P.Q | Q' | P.Q' | (P.Q)+(P.Q') | P |
|---|---|---|---|---|---|---|
| 0 | 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 1 | 1 | 1 | 1 |
| 1 | 1 | 1 | 0 | 0 | 1 | 1 |
From ISC 2018 Computer Science Paper 1, question 1(d).